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Properties

Label 74970b
Number of curves $2$
Conductor $74970$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 74970b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
74970.h2 74970b1 \([1, -1, 0, -3992235, -3294305659]\) \(-3038732943445107/267267200000\) \(-618906717392342400000\) \([2]\) \(3456000\) \(2.7334\) \(\Gamma_0(N)\)-optimal
74970.h1 74970b2 \([1, -1, 0, -65167755, -202469563675]\) \(13217291350697580147/90312500000\) \(209135325675937500000\) \([2]\) \(6912000\) \(3.0800\)  

Rank

sage: E.rank()
 

The elliptic curves in class 74970b have rank \(0\).

Complex multiplication

The elliptic curves in class 74970b do not have complex multiplication.

Modular form 74970.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 2 q^{11} + q^{16} - q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.